Binder Parameter of a Heisenberg Spin-Glass Model in Four Dimensions

Details Binder Parameter of a Heisenberg Spin-Glass Model in Four Dimensions Binder Parameter of a Heisenberg Spin-Glass Model in Four Dimensions

2002-11-23

arxiv.org/abs/cond-mat/0211521v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages including 4 figures, submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.67.100405

We studied the phase transition of the $\pm J$ Heisenberg model with and without a random anisotropy on four dimensional lattice $L\times L\times L\times (L+1)$ $(L\leq 9)$. We showed that the Binder parameters $g(L,T)$'s for different sizes do not cross even when the anisotropy is present. On the contrary, when a strong anisotropy exists, $g(L,T)$ exhibits a steep negative dip near the spin-glass phase transition temperature $T_{\rm SG}$ similarly to the $p-$state infinite-range Potts glass model with $p \geq 3$, in which the one-step replica-symmetry-breaking (RSB) occurs. We speculated that a one-step RSB-like state occurs below $T_{\rm SG}$, which breaks the usual crossing behavior of $g(L,T)$.

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